Basics of Geometry
This chapter introduces students to the basic elements of geometry, including points, lines, angles, and polygons. Also covered are bisectors, midpoints, and segments.
Reasoning and Proof
This chapter gives students an introduction to the concepts surrounding proofs. Included topics are inductive reasoning, conditional statements, and properties of congruence.
Parallel and Perpendicular Lines
This chapter covers the properties of parallel and perpendicular lines. Students are also exposed to more two-column proofs as well as a review of the algebraic equations of lines and slopes.
Triangles and Congruence
This chapter explores the properties of triangles, specifically their angles. Students learn the different methods used to determine congruency. Also covered is an introduction to isosceles and equilateral triangles.
Relationships with Triangles
This chapter allows students to further explore triangles through topics including mid-segments, perpendicular bisectors and angle bisectors, medians, and altitudes. Also considered are the relationships between the sides of different triangles.
Polygons and Quadrilaterals
This chapter delves into the properties of polygons and quadrilaterals, including parallelograms, rhombi, rectangles, squares, kites, and trapezoids. Students learn how to prove that different types of quadrilaterals are parallelograms.
After a brief review of ratios and proportions, this chapter covers the concept of similarity and applies it to polygons, quadrilaterals and triangles. It then extends proportionality to parallel lines and dilations and ends with fractals.
Right Triangle Trigonometry
This chapter proves the Pythagorean Theorem and its converse. It also introduces trigonometry ratios and covers an extension about the Law of Sines and the Law of Cosines.
This chapter covers all the parts of a circle and explores the properties of tangent lines, arcs, inscribed angles, chords, angles and segments that are formed by chords, tangents and secants, equations and graphs of circles.
Perimeter and Area
In this chapter, students learn how to find the perimeter and area of triangles, quadrilaterals, polygons, and circles.
Surface Area and Volume
This chapter extends what we know about two-dimensional figures to three-dimensional shapes. Different types of 3D shapes and their parts are defined. Then, surface area and volume of prisms, cylinders, pyramids, cones, and spheres are found.
The final chapter of Basic Geometry transforms a figure by moving, flipping, or rotating it. First, it looks at symmetry, followed by the different transformations.